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3-38.

Simplify the following fraction expressions. Show all of your work.  

  1. Diagram expression with 2 equal sized rectangles: Left Rectangle + Right Rectangle. Rectangle A, 4 rows, with 3 shaded. Rectangle B, 3 columns, with 2 shaded.

    Changes: Left rectangle, divided into 3 columns, 9 out of 12 shaded. Right column, divided into 4 rows, 8 out of 12 shaded.

    Draw diagrams to represent each fraction. Diagram expression with 2 equal sized rectangles: Left Rectangle + Right Rectangle. Rectangle A, 4 rows, with 3 shaded. Rectangle B, 3 columns, with 2 shaded.

    Now change the diagram so that each whole is divided into equal portions. Changes: Left rectangle, divided into 3 columns, 9 out of 12 shaded. Right column, divided into 4 rows, 8 out of 12 shaded.

  1. Follow the steps in part (a) to solve the problem.

  1. Draw a rectangle. 

    Rectangle divided vertically into 5 columns, with 3 shaded.

    Changes: Rectangle, divided into 3 rows, with first row shaded. The first 3 cells in the first row are shaded twice.

    Shade in three fifths. Rectangle divided vertically into 5 columns, with 3 shaded.

    Shade in one third in the other direction. Changes: Rectangle, divided into 3 rows, with first row shaded. The first 3 cells in the first row are shaded twice.

    The darker overlapping region is your answer.

  1. See part (c).